The better way to explain the concept of Buckling is with examples. Let’s dive in.
Imagine a long thin straw. Place it vertical on the table and try to hold it by placing your finger on the top. The straw will stand upright as it is expected.
Now, try to put a slight pressure on the straw by pressing your finger on the top. Still it stands… Now, keep on increasing the pressure. At some point, the straw will suddenly bend or wobble in the middle. This particular behavior in nutshell is called “Buckling” and this applies to our structural members as well.
It is the phenomenon where members suddenly fail by bending sideways even before the material itself breaks. It is just like our straw wobbling over, but for structural components.
Now, I consider we are somewhere near to understand buckling. Let’s get a little deeper.
Paper Straw & Spaghetti Noodles
Imagine we are having a “Paper Straw” and a “Spaghetti Noodles” (Its nothing but a long thin pasta).
Comparing these two, which will undergo buckling first. Nothing to think much, as it is evident to everyone, the “Spaghetti Noodle” will buckle first. But, WHY..? Because, it is SLENDER than the paper straw.
Interesting, how we declare a member as SLENDER.
Before moving to it, let’s consider one more example. Previously, the comparison is between two different materials (paper straw & spaghetti noodles). Now, let’s compare a “Paper Straw of 10 cm long” and a “Paper Straw of 20cm long”. Which one will buckle first..?
Obviously the longer one and the reason remains same. It is slender than the shorter straw.
If you look into these two examples in deep, we get to know how buckling works.
In the first example we compared two different materials. The material property might differ. For an argument sake, lets consider the straw is not made of paper and it is of pasta. Now, the materials are same, still the noodle will buckle first. It is because of the cross sectional property. Especially the “Radius of Gyration”. To explain radius of gyration in a simple statement, “It is the measure of how far the material from the centroid”. (Radius of Gyration itself is a huge topic to cover, so let’s not get into that and let’s try to focus on buckling and slenderness).
Okay. Now I could feel some of you arguing that, since the cross sectional area of the Straw and Noodle are different, the one with the higher cross sectional area would stand. Where do we get radius of gyration here..?
To answer this, let us have an another example. Now consider two straws made of paper (of same length), both of same cross sectional area but straw 1 has lower radius of gyration than straw 2. Which one will buckle first?
With the concept of radius of gyration, the straw which has lesser radius of gyration will buckle first, because the materials are nearer to the centroid compared to the other straw. So the member which have materials farther away from the centroid can withstand buckling more than the member (of same cross sectional area) which have materials nearer to the centroid.
Radius of Gyration in action:
To evidently prove this, kindly check the below table (TATA Structura Steel Brochure) and answer the this question, “Considering 40mm diameter pipes of 2.9mm thick, 3.2mm thick & 4mm thick, which one will take more load to buckle?”.
4mm thick pipe..? Nope.
If you see the radius of gyration of the different thicknesses. The 4mm thick tube has the least value comparing 3.2mm and 2.9mm. Obviously the 2.9mm pipe will take more load to buckle.
This proves that, comparing the members of same cross section, the member with lower radius of gyration will buckle first.
So, from our first case, we learnt how radius of gyration is related to buckling.
More Radius of Gyration means -> More load is required to buckle the member
Now moving to the next.
Comparing paper straws of 10cm and 20cm, the straw which is 10cm long will withstand buckling more than the 20cm. Since the longer one is slender and susceptible to wobble.
Why this happens?
As we mentioned earlier, buckling is simply bending sideways. Since we have more length, we have more room for bending in the longer straw than the shorter one.
Longer the Member -> More prone to buckling
Being said this, the slenderness of a member is measured by calculating the dimensionless quantity called the “Slenderness Ratio”, which is the ratio of Effective length of the member to its least radius of gyration.
Slenderness Ratio, λ = L / r
This particular value reflects the susceptibility of the member to buckling under compressive loads.
More the slenderness ratio, the member will subject to buckle at the earliest.
So, if we are trying avoid buckling in our structural member, we can achieve that by doing two things.
- Increasing the radius of gyration of the member.
- Reducing the length of the member.
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